Cyanobacteria are an integral part of Earth’s biogeochemical cycles and a promising resource for the synthesis of renewable bioproducts from atmospheric CO₂. Growth and metabolism of cyanobacteria are inherently tied to the diurnal rhythm of light availability. As yet, however, insight into the stoichiometric and energetic constraints of cyanobacterial diurnal growth is limited. Here, we develop a computational framework to investigate the optimal allocation of cellular resources during diurnal phototrophic growth using a genome-scale metabolic reconstruction of the cyanobacterium Synechococcus elongatus PCC 7942. We formulate phototrophic growth as an autocatalytic process and solve the resulting time-dependent resource allocation problem using constraint-based analysis. Based on a narrow and well-defined set of parameters, our approach results in an ab initio prediction of growth properties over a full diurnal cycle. The computational model allows us to study the optimality of metabolite partitioning during diurnal growth. The cyclic pattern of glycogen accumulation, an emergent property of the model, has timing characteristics that are in qualitative agreement with experimental findings. The approach presented here provides insight into the time-dependent resource allocation problem of phototrophic diurnal growth and may serve as a general framework to assess the optimality of metabolic strategies that evolved in phototrophic organisms under diurnal conditions.

The steady-state assumption, which states that the production and consumption of metabolites inside the cell are balanced, is one of the key aspects that makes an efficient analysis of genome-scale metabolic networks possible. It can be motivated from two different perspectives. In the time-scales perspective, we use the fact that metabolism is much faster than other cellular processes such as gene expression. Hence, the steady-state assumption is derived as a quasi-steady-state approximation of the metabolism that adapts to the changing cellular conditions. In this article we focus on the second perspective, stating that on the long run no metabolite can accumulate or deplete. In contrast to the first perspective it is not immediately clear how this perspective can be captured mathematically and what assumptions are required to obtain the steady-state condition. By presenting a mathematical framework based on the second perspective we demonstrate that the assumption of steady-state also applies to oscillating and growing systems without requiring quasi-steady-state at any time point. However, we also show that the average concentrations may not be compatible with the average fluxes. In summary, we establish a mathematical foundation for the steady-state assumption for long time periods that justifies its successful use in many applications. Furthermore, this mathematical foundation also pinpoints unintuitive effects in the integration of metabolite concentrations using nonlinear constraints into steady-state models for long time periods.

In this article, we present a protocol for generating a complete (genome-scale) metabolic resource allocation model, as well as a proposal for how to represent such models in the systems biology markup language (SBML). Such models are used to investigate enzyme levels and achievable growth rates in large-scale metabolic networks. Although the idea of metabolic resource allocation studies has been present in the field of systems biology for some years, no guidelines for generating such a model have been published up to now. This paper presents step-by-step instructions for building a (dynamic) resource allocation model, starting with prerequisites such as a genome-scale metabolic reconstruction, through building protein and noncatalytic biomass synthesis reactions and assigning turnover rates for each reaction. In addition, we explain how one can use SBML level 3 in combination with the flux balance constraints and our resource allocation modeling annotation to represent such models.

Microorganisms have developed complex regulatory features controlling their reaction and internal adaptation to changing environments. When modeling these organisms we usually do not have full understanding of the regulation and rely on substituting it with an optimization problem using a biologically reasonable objective function. The resulting constraint-based methods like the Flux Balance Analysis (FBA) and Resource Balance Analysis (RBA) have proven to be powerful tools to predict growth rates, by-products, and pathway usage for fixed environments. In this work, we focus on the dynamic enzyme-cost Flux Balance Analysis (deFBA), which models the environment, biomass products, and their composition dynamically and contains reaction rate constraints based on enzyme capacity. We extend the original deFBA formalism to include storage molecules and biomass-related maintenance costs. Furthermore, we present a novel usage of the receding prediction horizon as used in Model Predictive Control (MPC) in the deFBA framework, which we call the short-term deFBA (sdeFBA). This way we eliminate some mathematical artifacts arising from the formulation as an optimization problem and gain access to new applications in MPC schemes. A major contribution of this paper is also a systematic approach for choosing the prediction horizon and identifying conditions to ensure solutions grow exponentially. We showcase the effects of using the sdeFBA with different horizons through a numerical example.